Micromachined (MEMS) gyroscopes have become established as useful commercial items. Generally speaking, a MEMS gyroscope incorporates two high-performing MEMS devices, specifically a self-tuned resonator in the drive axis and a micro-acceleration sensor in the sensing axis. Gyroscope performance is very sensitive to such things as manufacturing variations, errors in packaging, driving, linear acceleration, and temperature, among other things. Basic principles of operation of angular-rate sensing gyroscopes are well understood and described in the prior art (e.g., Geen, J. et al., New iMEMS Angular-Rate-Sensing Gyroscope, Analog Devices, Inc., Analog Dialog 37-03 (2003), available at http://www.analog.com/library/analogDialogue/archives/37-03/gyro.html, which is hereby incorporated herein by reference in its entirety).
The principles of vibratory sensing angular rate gyroscopes with discrete masses are long-established (see, for example, Lyman, U.S. Pat. No. 2,309,853 and Lyman, U.S. Pat. No. 2,513,340, each of which is hereby incorporated herein by reference in its entirety). Generally speaking, a vibratory rate gyroscope works by oscillating a proof mass (also referred to herein as a “shuttle” or “resonator”). The oscillation is generated with a periodic force applied to a spring-mass-damper system at the resonant frequency. Operating at resonance allows the oscillation amplitude to be large relative to the force applied. When the gyroscope is rotated, Coriolis acceleration is generated on the oscillating proof mass in a direction orthogonal to both the driven oscillation and the rotation. The magnitude of Coriolis acceleration is proportional to both the velocity of the oscillating proof mass and the rotation rate. The resulting Coriolis acceleration can be measured by sensing the deflections of the proof mass. The electrical and mechanical structures used to sense such deflections of the proof mass are referred to generally as the accelerometer.
One of the more troubling manufacturing errors for micromachined gyroscopes is asymmetry of the sidewall angle produced during etching of the flexures. This tends to cross-couple the in-plane (X-Y axes) and out of plane (Z axis) motions. For example, in X-Y gyroscopes of the type described in U.S. Pat. Nos. 5,635,640, 5,869,760, 6,837,107, 6,505,511, 6,122,961, and 6,877,374, each of which is hereby incorporated herein by reference in its entirety, such asymmetry can result in a so-called “quadrature” interfering signal, a motion of the Coriolis accelerometer in phase with the resonator displacement. This cross coupling is nominally about 1% in typical production processes. Extraordinary production measures can reduce it to 0.1% but in processes optimized for high etching speed (and therefore low-cost) it can be as high as 5%. In contrast, the full scale signal of a low-cost consumer-grade gyro is typically only 0.001% and the required resolution might be 1,000 times to 10,000 times smaller than full scale. Thus, the interfering signal is comparatively large and places an almost impossible dynamic range requirement on the gyro electronics. The quadrature signal can be nulled with static trimming and a servo using appropriate electrodes, as described in other disclosures. However, the stability requirements of the trim and dynamic range of the servo are still very difficult electronics constraints with the tolerances accompanying high-speed mass production.
A symmetric structure with angular vibration in-plane (i.e. about the Z axis) produces Coriolis induced out-of-plane tilts (i.e., about X-Y axes). Generally speaking, the out-of-plane tilt produced by a flexure with bad sidewalls is about an axis perpendicular to the long dimension of the flexure.